Stability of solutions to inverse scattering problems with fixedenergy data
Abstract
A review of the author's results is given. Inversion formulas and stability estimates for the solutions to 3D inverse scattering problems with fixedenergy data are obtained. Inversions of exact and noisy data are stidied. The inverse potential scattering problem is discussed in detail, inversion formulas are derived and error estimates are obtained. Inverse obstacle scattering problem with data at a fixed frequency is studied. Uniqueness theorems and stability estimates are obtained. Inverse geophysical scattering problem is discussed. An algorithm for computing the DirichlettoNeumann map from the scattering amplitude and vicxe versa is obtained. An analytical example of nonuniqueness of the solution to a 3D inverse geophysical problem is constructed. An inverse problem for a parabolic equation is discussed.
 Publication:

arXiv eprints
 Pub Date:
 August 2000
 arXiv:
 arXiv:mathph/0008010
 Bibcode:
 2000math.ph...8010R
 Keywords:

 Mathematical Physics;
 Mathematics  Analysis of PDEs;
 Mathematics  Mathematical Physics;
 35R30;
 35R25;
 47H17;
 34C35;
 34G20